Metamath Proof Explorer


Theorem anbi1i

Description: Introduce a right conjunct to both sides of a logical equivalence. (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)

Ref Expression
Hypothesis anbi.1
|- ( ph <-> ps )
Assertion anbi1i
|- ( ( ph /\ ch ) <-> ( ps /\ ch ) )

Proof

Step Hyp Ref Expression
1 anbi.1
 |-  ( ph <-> ps )
2 1 a1i
 |-  ( ch -> ( ph <-> ps ) )
3 2 pm5.32ri
 |-  ( ( ph /\ ch ) <-> ( ps /\ ch ) )